L' Hospital's Rule

In this topic:

    (1) Evaluate the limit using L'Hospital's rule.

    (2) Evaluate the limit using L'Hospital's rule.

    (3) Evaluate the limit using L'Hospital's rule.

    (4) Evaluate the limit using L'Hospital's rule.  

    (5) Evaluate the limit using L'Hospital's rule.

    (6) Evaluate the limit using L'Hospital's rule.

    (7) Evaluate the limit using L'Hospital's rule.
    

Example (L'Hospital's Rule with Intermediate Form )  Evaluate the limit using L'Hospital's rule.

    Solution. The limit has the indeterminate form since and We try to use L'Hospital's rule to find,
    


Example (L'Hospital's Rule with Intermediate Form )  Evaluate the limit using L'Hospital's rule.

    Solution. The limit has the indeterminate form since and We try to use L'Hospital's rule to find,
    


Thus illustrating that L'Hopital's rule can be used multiple times.

Example (L'Hospital's Rule with Intermediate Form ) Evaluate the limit using L'Hospital's rule.

    Solution. The limit has the indeterminate form since and Suppose the limit exists, say Then,







Since and this limit has the indeterminate form of and so we try L'Hospital's rule,  








    

Example (L'Hospital's Rule with Intermediate Form ) Evaluate the limit using L'Hospital's rule.

    Solution. The limit has the indeterminate form since and Suppose the limit exists, say Then,










    

Example (L'Hospital's Rule with Intermediate Form ) Evaluate the limit using L'Hospital's rule.

    Solution. The limit has the indeterminate form since and Suppose the limit exists, say Then,









The limit has the indeterminate form since and So we try to use L'Hospital's rule to find,

  

Example (L'Hospital's with Rule Intermediate Form ) Evaluate the limit using L'Hospital's rule.

    Solution. The limit has the indeterminate form since and We try L'Hospital's rule to find,

  

Example (L'Hospital's Rule with Intermediate Form ) Evaluate the limit using L'Hospital's rule.

    Solution. Let's make a change of variable to simply the express, namely Since as we have







The limit has an indeterminate form and so we try L'Hopital's rule,

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L Hospital Rule
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
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